The input terminal(s) of an LNA often has to be matched to the resistance of the signal source driving the LNA. A commonly employed method of generating the required input resistance is inductive source degeneration. The input stage of a cascoded differential MOS LNA is depicted in FIG. 1. In the figure MOSFETs M3 and M4 act as cascodes to MOSFETs M1 and M2 respectively and have their gates connected to a constant bias voltage.
The input impedance of a pure MOSFET when driven at the gate is mainly capacitive. Therefore some form of feedback has to be employed in order to generate a real input impedance when using a MOSFET that is driven at the gate. The impedance of the RF+ input in the circuit of FIG. 1 has a real component due to the fact that the MOSFET exhibits a phase lag between its gate and source. As a result the phase contributions of the inductor at the source of M1 is reduced by 90° when viewed at its gate. Analysing the small signal model of the circuit of FIG. 1 yields the following result for the input impedance of M11: The effects of the gate-drain capacitance of M1 (Cgd1) has been ignored here for simplicity. Since the MOSFET is cascoded ignoring Cgd1 will not alter the above result much.
      Z          in      ⁢                          ⁢      1        =                              g                      m            ⁢                                                  ⁢            1                          ⁢                  L                      s            ⁢                                                  ⁢            1                                      C                  gs          ⁢                                          ⁢          1                      +          j      ⁡              (                              ω            ⁢                                                  ⁢                          L                              s                ⁢                                                                  ⁢                1                                              -                      1                          ω              ⁢                                                          ⁢                              C                                  gs                  ⁢                                                                          ⁢                  1                                                                    )            
The effect of the source degeneration inductance Ls1 (90° phase lead) has been to appear as a real input resistance of
            g              m        ⁢                                  ⁢        1              ⁢          L              s        ⁢                                  ⁢        1                  C          gs      ⁢                          ⁢      1      (no phase lead). The input resistance of the LNA as presented in the above equation is not purely resistive and contains a reactive element. This reactive element vanishes at the resonance frequency of the LNA.
In the preceding arguments and circuit diagrams the active device used is a MOSFET. It should be pointed out that all the preceding arguments apply even when the LNA uses bipolar transistors. Even though bipolar devices already possess a real input resistance on their own (as opposed to capacitive in the case of a MOSFET), quite often it might still be required to use inductive degeneration to supplement the input resistance of the device as well as improve the linearity of the circuit. This leads to a circuit similar to that in FIG. 1, but with all the MOSFETs replaced by bipolar transistors.
Quite often LNAs have to be capable of processing a wide dynamic range of signals. When input signals are small the LNA should have a high gain and low noise figure, while linearity is not as important. When input signals are large the LNA should have a low gain and high linearity, while noise figure is not as important. This places conflicting demands on the design of the transconductance of M1 and M2 (gm1 in the above equation).
In order to obtain a good gain and noise figure gm1 should be maximised with a small gate-source overdrive. This limits the linearity of the circuit. It is possible to use the inductive degeneration already present in the circuit to help improve the linearity somewhat. Nonetheless, in order to obtain a very high linearity and low gain gm1 should be minimised with a large gate-source overdrive. Thus it is important to be able to modify gm1 in order to optimise the LNA for either noise figure or linearity for high dynamic range operation.
If gm1 is changed by modifying the bias current of M1 the input resistance of the circuit immediately changes as well. This is predicted by the above equation for Zin1. This destroys the input impedance match of the LNA. Input impedance matching is very important, especially if the LNA is driven by SAW filters.